Answer:
407.22 foot is the boat from the base of the lighthouse
Step-by-step explanation:
Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.
Let x foot be the distance of the object(boat) from the base of the lighthouse
Angle of depression = ![7^{\circ}](https://tex.z-dn.net/?f=7%5E%7B%5Ccirc%7D)
[Alternate angle]
In triangle CAB:
To find AB = x foot.
Using tangent ratio:
![\tan (\theta) = \frac{Opposite side}{Adjacent Base}](https://tex.z-dn.net/?f=%5Ctan%20%28%5Ctheta%29%20%3D%20%5Cfrac%7BOpposite%20side%7D%7BAdjacent%20Base%7D)
![\tan (\angle CAB) = \frac{BC}{AB}](https://tex.z-dn.net/?f=%5Ctan%20%28%5Cangle%20CAB%29%20%3D%20%5Cfrac%7BBC%7D%7BAB%7D)
Here, BC = 50 foot and ![\angle CAB =7^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20CAB%20%3D7%5E%7B%5Ccirc%7D)
then;
![\tan (7^{\circ}) = \frac{50}{x}](https://tex.z-dn.net/?f=%5Ctan%20%287%5E%7B%5Ccirc%7D%29%20%3D%20%5Cfrac%7B50%7D%7Bx%7D)
or
![x = \frac{50}{\tan 7^{\circ}}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B50%7D%7B%5Ctan%207%5E%7B%5Ccirc%7D%7D)
![x = \frac{50}{0.1227845609}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B50%7D%7B0.1227845609%7D)
Simplify:
AB = x = 407.217321 foot
Therefore, the boat from the base of the light house is, 407.22'
Answer:
your answer is 4/13ths. #markasbrainliest
Answer:
<em>x = 9</em>
Step-by-step explanation:
The standard form of equation of a line is expressed as y = mx+c
m is the slope
c is the y intercept
Note that the line does not have a slope and the x intercept of the line is a point where the line cuts the x axis. Hence the equation of the line will be expressed as x = c where c is the x intercept;
<em>From the graph, the x intercept =9. Hence the equation of the given line is x = 9</em>
-4,6) (8,-12)
square root of 12^2+-18^2
<span>square root of 144+324
</span><span>square root of 468
21.63
</span>